Attractors and first order formalism in five dimensions revisited

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five-dimensional rotating black object potential depending on Taub-Newman-Unti-Tamburino, electric and magnetic charges as well as on all the scalar and gauge fields, is investigated. The first order formalism in d = 5 is constructed and analyzed. We derive a general expression defining the fake superpotential which is valid for all charge configurations. An explicit expression for the fake superpotential is constructed, for all very special geometries, in the case of vanishing Taub-Newman-Unti-Tamburino charge. We carry out an analogous construction in the very special geometries corresponding to t(3) and stu models, for the most general charge configurations. The attractor flows and horizon values of all fields are given.